Local scaling limits of Lévy driven fractional random fields

Scaling limits for random fields with long-range dependence

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Local limits of random graphs

A graph G is a couple G = (V, E) where V denotes the set of vertices of G and V the set of undirected edges. We will assume that the graphs considered are simple, that is they do not have multiple edge nor loop. The degree deg(v) of a vertex v of G is the number of edges attached to v. In the following except explicitly mentioned all the graphs considered are locally finite (no vertex of infini...

Multi-operator Scaling Random Fields

In this paper, we define and study a new class of random fields called harmonizable multi-operator scaling stable random fields. These fields satisfy a local asymptotic operator scaling property which generalizes both the local asymptotic self-similarity property and the operator scaling property. Actually, they locally look like operator scaling random fields whose order is allowed to vary alo...

Scaling limits of large random trees

The goal of these lectures is to survey some of the recent progress on the description of largescale structure of random trees. We will use the framework of Markov branching sequences of trees and develop several applications, to combinatorial trees, Galton-Watson trees, some dynamical models of randomly growing trees, cut trees, etc. This is a rough draft – to be completed – all comments are w...

Random fractals and scaling limits in percolation